The mathptmx package is not the best way to load the times font as the fonts are both incomplete and a patchwork of symbols from different sources.
Among the free fonts, you best choice today is probably newtx (alternatively, on older distributions, you have txfonts, but they have some spacing problems):

\documentclass{article}
\usepackage{newtxtext}
\usepackage{newtxmath}
\begin{document}
$y = f(x)$
$\mathbf{y=f(x)}$
{\boldmath$y=f(x)$}
\end{document}
For the sake of closing this question, here is a summary of the comments:
fontenc
and inputenc
are incompatible with fontspec
.
fontspec
with xe
- / lualatex
fontspec
lets you use any TrueType and OpenType font easily (with commands like \setmainsfont
that just need the name of the font you want to use), but require you to compile your document with a modern TeX engine such as xelatex
or lualatex
. These two engines in return forces you to use utf8
encoding, and are therefore incompatible with \inputenc
. Also, as fontspec
is a kinda upgrade to fontenc
, you shouldn't load fontenc
either.
For more information on xelatex
/ lualatex
vs pdflatex
, read these questions:
fontenc
with pdflatex
If for some reason you want or need to compile with the legacy pdflatex
, you will need to find a font that is available in Type1 format, and load it "the old way".
The best option seem to be TeX Gyre Termes, loaded by the tgtermes
package. Part of the modern TeX Gyre collection of fonts, an initiative aimed at providing high quality versions of standard fonts for TeX and in OpenType format, it is a replacement for the older URW Nimbus Roman font, that can be loaded by the mathptmx
package (AFAIK, mathptmx
is nimbus
with math support added, but I might be wrong).
Another option is the New TX font, loaded by the newtxtext
and newtxmath
packages (you need to load both).
Note that for both these options you should also switch to Cork font encoding, i.e. \usepackage[T1]{fontenc}
.
For more about Times replacement, you can read What is going on with all these Times clones?
Best Answer
The
txfonts
package used to be the answer, but since some days a new package has been developed based on the first one, with new metric files for fonts that should avoid some of the weaknesses shown bytxfonts
:mathptmx
txfonts
newtxmath
A word of advice about the TeX distribution: disk space is not a big issue nowadays. Unless you're running TeX on a very small device, do a full install.